A guy wire is attached to the top of a radio antenna and to a point on horizontal ground that 40 m from the base of the antenna. If the wire makes an angle of 58deg 20min with the group find the length of the wire.
Accepted Solution
A:
Answer:The length of the wire is 76.19 m.Step-by-step explanation:It is given that a guy wire is attached to the top of a radio antenna and to a point on horizontal ground that 40 m from the base of the antenna. It means base of the right angled triangle is 40 m.The wire makes an angle of 58deg 20min with the ground.1 degree = 60 minUsing this conversion convert the given angle in degree.[tex]58^{\circ}20'=58^{\circ}\frac{20}{60}^{\circ}=58\frac{1}{3}^{\circ}=\frac{175}{3}^{\circ}[/tex]In a right angled triangle[tex]\cos \theta=\frac{adjacent}{hypotenuse}[/tex][tex]\cos (\frac{175}{3}^{\circ})=\frac{40}{hypotenuse}[/tex][tex]0.525=\frac{40}{hypotenuse}[/tex][tex]hypotenuse=\frac{40}{0.525}[/tex][tex]hypotenuse=76.190[/tex]Therefore the length of the wire is 76.19 m.